Beethoven moved to Vienna in 1792, a few weeks before his 22nd birthday, and sought out Haydn for lessons. The figure who was notably absent from Vienna was Mozart, who had died a year earlier. Beethoven soon established himself as Vienna's best pianist, just as Mozart had done upon moving to Vienna in 1781. For both Mozart and Beethoven, their reputations as composers lagged behind their performing careers. Mozart finally won over Vienna with the 15 new piano concertos he debuted on his own concerts between 1782 and 1786. Beethoven also performed as the soloist in his own concertos, and his first two efforts, composed in the 1790's, worked admirably from the Mozart mold.

Beethoven composed the bulk of the third concerto in 1800, in time for a major debut concert in Vienna, but he chose to play an earlier concerto instead. After a few more years of tinkering, he unveiled the new concerto on an 1803 program that also included the premieres of the Second Symphony and the oratorio Christ on the Mount of Olives as well as a reprise performance of the First Symphony. On the day of the concert, Beethoven awoke at five to copy out trombone parts; then he led the program's only rehearsals, starting at eight until breaking in the afternoon for snacks and wine; he led one more run-through of the oratorio for good measure; finally, after a short interval, he commenced the performance at six that evening. For the concerto, Beethoven performed off of a hastily written score that, in the words of his page turner, contained "almost nothing but empty leaves; at the most, on one page or another a few Egyptian hieroglyphs wholly unintelligible to me were scribbled down to serve as clues for him."

The Concerto's opening measures have a balanced, Classical flavor, with a string statement in the home key matched by a wind response that introduces the questioning note of the dominant key. True to Beethoven's emerging "middle" period style, the themes separate into essential fragments to be examined from all angles, with various rising triads, falling scales, and timpani-like alternations appearing in the foreground and background. There are also remnants of "early" Beethoven in the concerto, as in the graceful second theme and the effortless piano figurations and interplay. There are even hints of the intimate pathos of "late" Beethoven, especially in the otherworldly return of the orchestra after the cadenza.

The first E-major chord of the Largo movement could hardly be more alien, or more luminous. The movement continues as a study in contradictions: humble yet ornate, foreign yet familiar, slow yet restless. A telling exchange occurs between the flute and bassoon, trading childlike melodies over a simple plucked background, while the piano issues gusts of sound blurred by the sustain pedal. The unexplained setting of E-major makes more sense with the start of the finale, which emphasizes the melodic note A-flat, a respelling of the prominent G-sharp from the slow movement's home triad. Later in the movement, a sober fugal passage dissipates into an A-flat repeated in octaves, and the same musical pun recasts that note as G-sharp in an E-major passage that puts a radiant new spin on the movement's central theme. It is a sly and elegant move, handled with as much facility as Mozart, but reflecting a muscular willfulness that was pure Beethoven.